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The best time to undergo this task is while the clematis is still dormant. You can try untangling the clematis, replace the trellis and then tie the vine onto the new trellis. If this task is too frustrating (which it can be depending on how entwined your clematis is on your trellis) you can severely prune your clematis (while it is dormant) to remove it from its existing trellis. Just keep in mind that severe pruning may affect your next flower yield, but it will bloom nicely thereafter after it sends out new shoots from the base. If your clematis is not dormant, try propping up your trellis with stakes or other supports just to get it through the growing season, at which time you can try untangling or pruning.

For more information on growing clematis, please visit the following link:
https://www.gardeningknowhow.com/ornamental/vines/clematis/growing-clematis.htm